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LOCATIONS´RATIOS
Ratios
They result from a system of calculation based on the ratios which helped to decide the length of the bases of each of the three great pyramids,
then by combining the values of the length of the bases and the heights to determine the reciprocal implementations of the pyramids as indicated below.
(Values reported by William Matthew Flinders Petrie ).
(The method of determining the places of reciprocal implantation of the three great pyramids by means of a system calculated essentially based on the dimensions of the three pyramids,
including the height and length of the bases, demonstrating that all locations of the achitectural Giza Plateau set were simultaneously predetermined from the beginning
although their realization continued during successive reigns.
The simple fact that the size of the first interval, which separates from East to West Khufu Cheops, is one third of the sum of
basic lengths of Cheops and Mykerinus, - (a + c) / 3 = 213.75 -, is sufficient to show that the dimensions of Mykerinus were determined even before the beginning of Khafre's construction ...
Lenght in
"Cubits (Cr)" (1 Cr equals 0.5236 of our meters.)
© Reproduction prohibited without permission.
WHEN THEY EXIST, DIFFERENCES FROM MEASUREMENTS PUBLISHED BY PETRIE ARE REPORTED BY SHOWING THOSE OF PETRIE IN COLOR BROWN / RED.
The difference between Petrie's physical measurements and our method is never greater than 1 meter for a survey of nearly a kilometer ...
In Blue, the values of the same survey with the values we used to explain the relationships between the three great pyramids.
612/5000
Base lengths as measured by William Matthew Flinders Petrie:
a = Cheops = 439.81 cubits, used 440 Cr
b = Chephren = 411 cubits, used 410 Cr
c = Mykerinos = 201,44 cubits, used 200 Cr.
The implantation of the Pyramids as above shows clearly that it is not a coincidence but of a system of proportions calculated
essentially on the value of the length and heights of the bases of the pyramids:
All dimensions are strictly related,
this in all four directions, which once again confirms that Mykerinos was very present from conception!
Our paperwork, which was published in 2003, then in 2015 and today in 2019, was and still does reflect this consistency of relationships for all the measures
that necessarily resulted from a single overall design expected
from the very beginning simultaneously for the three pyramids.
To consult the relations of the lengths of bases,
cliqk here
Proportions of the pyramids
Fortunately, Ancient Egypt did not know the division, and that to calculate its proportions, they had invented the Egyptian Fractions.
In short, and an example will follow, these fractions constitute a sum of fractions whose numerator is equal to 1 and the denominator a positive integer, sometimes called "a development of Egyptian Fractions"
resulting from the decomposition of the ratio of two integers whose numerator is less than the denominator.
Two identical fractions cannot be repeated in development, however.
Example Khéops, with its size of 280/440.
Nowadays, the result for us is 7/11 or 0.636.364 which we can consider as "close to", but not exactly 2/3
The two dimensions are broken down into:
height 280 divisible by 5 and 7
and for the base 440 divisible by 5 and 11
This results in the report of 7/11
If we use the knowledge of Ancient Egypt, the development according to the Egyptian Fractions will be:
280/440 = 7/11 = + 1/2 + 1/9 + 1 / 1.160
This same report can be written in an infinite number of ways, for example:
7/11 = + 1/2 + 1/8 + 1/129 + 1 / 18.875
7/11 = + 1/2 + 1/8 + 1/128
A rounding rule consisted in reducing by 1 the denominator of the last fraction that we wanted to keep, and in this case we get:
7/11 = + 1/2 + 1/7
The Egyptian fractions applied to the three pyramids will bring us a very particular light, by attracting your
be careful that the base of Chephren is measured for 411 cubits, and not 410, as practiced by current usage, even for Mykerinos the actual measurement is 201.44 cubits and not 200 as in current usage .
We then obtain the following results:
Khéphren Height / base: 275/411 = 1/2 + 1/6
Khéops Height / base: 280/440 = 1/2 + 1/7
Mykérinos Height / base: 125/201 = 1/2 + 1/8
| The reciprocal proportions of the three pyramids The choice of dimensions, the Why and the How of the reciprocal proportions the three great pyramids were decided and
calculated according to a common propor tion system. (5 minutes 06).
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we wrote during 2003 on this subject:
Among the Numbers used
Note: A prime number is a number which is only divisible by itself or by 1. Example: 2,3,5,7,11
The usual values that we know are the dimensions of the pyramids (280/440, 275/410 and 125/200).
We had submitted a response with frames. It is not they which are important, it is the system which is not only wanted but designed to transmit knowledge.
During 2003 we used a frame of 350 cubits subdivided into 11 times 30 and once 20, which can also be written as a frame of 2x5x5x7
subdivided into 11 times 2x3x5 and once 2x2x5
If the question seemed unanswered, there is at least one , but which implies going to other methods, and mathematicians will quickly recognize the analogies with
"Euclid's algorithm" and its positive and negative recursion.
This line of research, although seeming coherent was not enough, it was only a mathematical result of the system as some may find Pi, Phi or other constants.
We have always researched only by using their procedures, knowledge, or methods in order to see the answers appear if there were any and we can say today after several decades of practice
that even with a computer, not much would have been obvious.
Surprising? No, correct, yes! (your smartphone calculator is enough ...)
Analyzing their achievements according to their methods has always pleased us because they are very meaningful to our mind and in three lines we learn or understand more than with many pages,
as well as with proportions as opposed to absolute values.
Updates 2015-2020:
What can we also see at a glance?
That the three pyramids with different dimensions are all three in the same proportion ratio very very close to 2/3 (0.6666666) and that Khépren answers them very exactly when we would be more inclined to
think that Cheops held perfection ...
Even more interesting: the only variable complements of the constant ratio 1/2 are constituted by 1/6, 1/7, 1/8, and there, in our only and modest opinion we think that this is the objective that determined
the physical dimensions of the pyramids in a constant proportion ratio although with a physical reality of simple to double ...
We summarize:
Apart from the "Why" of the pyramids, in terms of "How" we can say that:
The choice of the three proportions, was the first founding act of the three great pyramids of Giza,
Choice which was followed by that of their heights, the initial key height being that of Cheops: 10 times the perfect number 28 height from which the game of proportions determined the value of
its base, but also the heights and bases of the other two.
From the report of the previous two, it resulted in the size of each of the three bases.
These values ??of the dimensions once established then lead to the reciprocal positioning of the pyramids such as we explained it
see supra.
This system does not stop there and, to save you the calculation, to give you a complementary example, let us consider the East-West width ratio of the perimeter rectangle of the pyramids 1419 . along its North-South length 1732
1419/1732 = 71/87 and in Egyptian fractions can be written: 1/2 + 1/3 or 0.666666
According to our current mathematics:
1419/1732 = 0.81928 which according to our current rounding rules must be written: 0.82
or 1419/1732 = 71/87 = 1/2 + 1/4 + 1/14 which according to our current rounding rules must be written: 0.819 and which could also to write reduced to two Egyptian fractions: 1/2 + 1/3 = 0.833
Its diagonal in relation to its width will be written 1419/2239 or 1/2 + 1/8 + 1/124 reducible in two Egyptian fracytions 1/2 + 1 / 7 = 0.642
Its diagonal to its length will be written 1732/2239 or 1/2 + 1/4 + 1/44 which can be reduced to two Egyptian fractions 1/2 + 1/3 = 0.833.
EVERYTHING are only proportions for these three pyramids. You have just noticed some of them ..., there are many others in perfect consistency.
(Didn't our friend Pythagoras say that: "Everything is arranged according to numbers" ?).
Whoever discovers Giza is first of all challenged, - in addition to gigantism -, by the fact that the three pyramids are similar in their proportions although having different dimensions.
This is what, combined with the lack of alignment of the three pyramids, can lead to a first questioning ,
Khéops and its mathematical architecture is another,
Khéphren did not appear to us until much later.
If the three pyramids are in a ratio close to 2/3, Kephren is the only one to have it in a perfect way: 1/2 + 1/6 is 0.666666 ....
It also contains the values ??common to the three pyramids and one of our regrets will remain for not having studied it further.
This pyramid leaves us with the impression that our mind has been occupied by Cheops while, as in the hand of a conjurer, at the same time, it is the other who performs the trick .
Mykérinos requires only two prime numbers, 2 and 5, while the values ??of the other two pyramids require the use of the five prime numbers.
Its height is written 5x5x5 (We would say a power to the cube).
Its base is written: 2x2x2x5x5 (we would say today a cubic power by a square power).
The heights / bases proportions are 7/11 for Cheops and 8/11 for Mykerinos.
And we can simply notice that the height of Mykerinos is in the 5/11 ratio with that of Khéphren.
What we can really infer is that:
- the pyramids lead us to questioning
- 4,500 years ago, Ancient Egypt already had a perfect knowledge of numbers and proportions and had established reliable methods to use them,
- They put it in stone to testify and transmit it in addition to many other knowledge
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